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MHTCET 18 Apr 2026 Shift 2 Paper

Question : 146 of 150

Marks: +1, -0

2 x=3 y=-z

6 x=-y=-4 z

is …

Solution:

Concept:

Find direction ratios of both lines, then use

\cos \theta = \dfrac{a_1 a_2 + b_1 b_2 + c_1 c_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}

Explanation:

For

2x = 3y = -z = \lambda

, we get

x = \frac{\lambda}{2}, y = \frac{\lambda}{3}, z = -\lambda

So direction ratios are

(3, 2, -6)

after multiplying by 6.

For

6x = -y = -4z = \mu

, we get

x = \frac{\mu}{6}, y = -\mu, z = -\frac{\mu}{4}

So direction ratios are

(2, -12, -3)

after multiplying by 12.

Dot product:

3(2) + 2(-12) + (-6)(-3) = 6 - 24 + 18 = 0

Since dot product is zero, the lines are perpendicular.

Hence

\theta = \frac{\pi}{2}

Answer:

\frac{\pi}{2}

(Option D)

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